Tadic, who joins the Saints for an undisclosed fee, is new manager Ronald Koeman's first signing at St Mary's Stadium.
"It is a really nice feeling to sign. This is a really nice club of which I have heard a lot of good things about," he told Southampton's official website.
"I have already seen the beautiful training centre and there are lots of nice people that work here including the coaches so I am really happy to be here."
Tadic, who has spent the past two years at Twente, scored 16 goals in 33 games for the Dutch side last season.